Introduction
Dihydroxylation is a chemical transformation that converts an alkene into a vicinal diol. This oxidation process is typically achieved using transition metals in a high oxidation state, such as osmium or manganese, which often act as catalysts in the presence of another stoichiometric oxidant.
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The mechanism of dihydroxylation begins with the coordination of a ligand to the metal catalyst, for instance, osmium. Following this, the alkene coordinates to the metal via a (3+2) cycloaddition, leading to the dissociation of the ligand from the metal catalyst. The subsequent hydrolysis of the olefin produces the vicinal diol, and the catalyst is regenerated through oxidation by a stoichiometric oxidant, allowing the cycle to continue.
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Osmium tetroxide (OsO4) is a widely used oxidant in the dihydroxylation of alkenes due to its reliability and efficiency in producing syn-diols. However, due to its high cost and toxicity, only catalytic quantities of OsO4 are used, supplemented by a stoichiometric oxidizing agent. Manganese is another metal used in dihydroxylation. Its high oxidation potential can, however, lead to the over-oxidation of substrates.
Reaction
Reaction using osmium tetroxide:

Reaction using potassium permanganate:

Mechanism
Please note that these are simplified mechanisms which don't go into the details of the metal catalytic cycle which involves steps such as coordination, migratory insertion, reductive elimination, etc.
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Mechanism using osmium tetroxide:

Mechanism using potassium permanganate:
